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C5×C29×C3⋊D21 #32912529

order18270
automorphism?
homologyAbelianization (H1) = C2×C5×C29 · Schur multiplier (H2) = C3

Aliases

direct productC5×C29×C3⋊D21
unambiguous semidirect productC3⋊(C5×C29×D21)
unambiguous semidirect productC7⋊(C5×C3⋊D3×C29)

Splittings

Fitting, socle, HallC32×C5×C7×C29 ⋊ C2
derived, HallC32×C7 ⋊ C2×C5×C29
HallC32×C7×C29 ⋊ C2×C5
HallC32×C5×C29 ⋊ D7
HallC5×C7×C29 ⋊ C3⋊D3
HallC32×C5×C7 ⋊ C2×C29
HallC32×C29 ⋊ C5×D7
HallC7×C29 ⋊ C5×C3⋊D3
HallC32×C5 ⋊ D7×C29
HallC5×C7 ⋊ C3⋊D3×C29
SylowC32 ⋊ C5×D7×C29
SylowC7 ⋊ C5×C3⋊D3×C29

Subgroups

subgroupG/H
center, hypercenterC5×C29C3⋊D21
commutator, cosocle, hypocenterC32×C7C2×C5×C29
FrattiniC1G
Fitting, socleC32×C5×C7×C29C2
LCSG ▷ C32×C7
UCSC1 ◁ C5×C29

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9135

Conjugacy classes & character table

4785 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D3×C29×D21, C5×D87⋊D21, C29×D15⋊D21, …
maximal normal subgroup ofC5×D3×C29×D21, C5×D87⋊D21, C29×D15⋊D21, …
maximal quotient ofC5×C29×C3⋊Dic21, C2×C5×C29×C3⋊D21

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 67);